One of the challenges in personal positioning is to provide accurate position information in situations where there are only a few measurement sources available that might have large errors with unusual distributions, particularly indoors or in urban areas, requiring the efficient numerical solution of the nonlinear filtering equations resulting from the fusion of these different measurement sources. In these cases, it is advantageous that the maximum amount of information be extracted from every measurement.
The behaviour of satellite-based systems such as GPS is unpredictable at best when used indoors in high-sensitivity mode. Local wireless networks, such as the cellular network, WLAN or Bluetooth offer some positioning capability but with inferior accuracy when compared to GPS. Other possible components of a mobile electronic device are the on-board sensors such as accelerometers, barometers or digital compasses.
Combining the various measurement sources is difficult because of different error characteristics, unpredictable distortions, systematic errors in measurements, strong nonlinearity, complex time dependencies, and missing data. It is not simple to model all the cases in a general way, let alone solve the models accurately. Even with correct models, the commonly used Kalman filter and its nonlinear extensions can fail without warning.